In wireless communications, fixed-point complex ICA methods have been applied to perform separation of complex valued signals in a time variant environment in which various components of signals, or the signal per se, is time variant. Such ICA methods suffer from various limitations where the channel is constantly or abruptly changing. For adaptive filtering applications such as beamforming and system identification, and the Complex LMS method has been widely used both in block and sequential mode, due to its computational simplicity and relative ease of implementation. However, the main drawback of the Complex LMS method is its slow convergence. In addition, the performance is highly dependent on the choice of the convergence factor or learning rate which is constant and has to be manually selected by trial and error depending on the type of application. Furthermore, an incorrect choice of convergence factor could even result in divergence. Various methods of adaptive filtering or processing of such complex signals in time variant channels have been suggested in the art, these, for example, including:
1. LMS—an algorithm when slow convergence is not a major issue (typically used).
2. NLMS—simple extension of the LMS with much faster convergence in many cases (commonly used).
3. Frequency-domain methods—offer computational savings for long filters and usually offer faster convergence commonly used when there are already FFTs in the system.
4. Lattice methods—are stable and converge quickly, but cost substantially more than LMS and have higher residual MSE than other methods (occasionally used).
5. RLS—algorithms that converge quickly and are stable. However, they are considerably more expensive than LMS (almost never used).
6. Block RLS—(least squares) methods, which can be efficient in some cases (occasionally used).
7. IIR—Difficult to implement successfully, but used in some applications, for example noise cancellation of low frequency noise.
8. CMA—useful when applicable to (blind equalization); CMA is preferred method for blind equalizer initialization (commonly used in specific equalization applications).
A block adaptive method for gradient based ICA has been proposed by one of the within co-inventors (W. Mikhael). See Mikhael and Yang: “Optimum Block Adaptive (OBA) Algorithm for Gradient Based ICA for Time Varying Wireless Channels.” Proc 62 IEEE Vehicular Technology Conf., Dallas, Tex., USA, September 2005. Said paper teaches a fixed point ICA analysis method which includes an optimum block adaptive aspect. The so-called OBA/ICA is capable of tracking time variation. Simulation results from mobile telecommunication applications thereof indicate the resulting performance, particularly, with respect to convergence properties, is superior to fast-ICA under dynamic channel conditions.
Unlike the OBA/ICA, the Complex IA-ICA has the capability to process complex signals. The need for such improvement is attributable to the fact that complex signal processing systems do not possess sufficient degrees of freedom in certain applications. Due to this, there is a constant need for systems capable of adapting, in real time, to rapid and abrupt channel spatial and other changes. Although the prior art, as best known to the within inventors includes the 2000 publication of Bingham and Hyvarinen: “A Fast Fixed Point Algorithm for ICA of Complex Valued Signals.” Int. J. Neural Syst., 2000, 10, 1, pp. 1-8. Bingham et al teaches ICA as an improved statistical method for transforming an observed multidimensional random vector into components that are mutually as independent as possible. Therein, in the prior art, a fast fixed point algorithm was capable of separating complex values of mixed source signals as they existed at that time, and with a computational efficiency considered reasonable for the state-of-art in 1999. Today's needs however are different.
Applicable issues associated with adaptive signal filtering and processing are addressed by U.S. Pat. No. 5,805,481 (1998) to Raghunath, entitled Update Block for an Adaptive Equalizer Filter Configuration Capable of Processing Complex-Valued Coefficient Signals; U.S. Pat. No. 6,381,623 (2002) to Schenk, entitled Method for Adaptive Filter Adjustment in a QAM/Cap System; U.S. Application Publication US/2004/0171385 A1 (2004) to Haustein et al, entitled Adaptive Signal Processing Method in a MIMO-System; U.S. Pat. No. 7,061,977 (2006) to Martin et al, entitled Apparatus and Method for Using Adaptive Algorithms to Exploit Sparsity in Target Weight Vectors in an Adaptive Channel Equalizer and U.S. Pat. No. 7,170,924 (2007) to Corbaton, each relative to adaptive methods for adjustment of weight vectors.
None of the above art however suggests the novel methods of adaptive signal processing set forth herein.
Prior art wireless systems, employing complex fast ICA are highly efficient and popular in applications involving the separation of complex signals. Their performance however degrades in time-varying channel situations. In practice, such situations frequently arise in wireless communications when the signal propagates between the transmitter and receiver many factors may of course intervene to corrupt the signal. Therefore, prior art complex fast ICA methods are impractical in certain real time applications. It has been found that the present inventive method employing our novel complex IA-ICA technique functions successfully under both slow and abrupt variations in complex wireless channels.
The within inventors have authored the article entitled “Fast-Converging Complex Adaptive Algorithm for Diversity Wireless Receivers in Linearly Fading Channels, Electronic Letters, Vol. 42, No. 15 (Jul. 20, 2006) which was originally addressed in the provisional application to which this application claims priority. In 2008, the within inventors also authored the article “Complex Adaptive FIR Adaptive Filtering algorithm with Time-Varying Independent Convergence Factors,” which was published in Signal Processing, Volume 88, Issue 7, January 2008, pp. 1889-1893.
Other adaptive systems employing the Complex Least Mean Square (Complex LMS) method in both block mode and sequential mode have been widely used in various adaptive filtering applications because of its computational simplicity and relative ease of implementation. However, the inherent limitation of the Complex LMS is its dependence on the convergence factor or step size, which their fixed and has to be manually selected depending on the type of application or nature of the input signal. Moreover, a small step size results in slow convergence, and a large step size could cause unstable gradient descent, leading to divergence. Hence, the optimal convergence factor has to be chosen by trial and error. The invented adaptive systems employing our novel Complex OBA-LMS, Complex OBAI-LMS, Complex HA-LMS, and Complex IA-LMS techniques yield excellent convergence properties, in terms of convergence speed and accuracy.
The instant improvement will, it is anticipated, find important application in areas, including, without limitation, communications, speech identification, system modeling, event prediction, line quality enhancement, signal equalization, audio, speech and video processing. Generally, interference suppression in wireless communications, system identification, system modeling, predictive algorithms, and the above areas will all benefit from the cost and functionally efficient interference suppression accomplished by the present invention.